A primal-dual interior-point relaxation method with adaptively updating barrier for nonlinear programs

Abstract

Based on solving an equivalent parametric equality constrained mini-max problem of the classic logarithmic-barrier subproblem, we present a novel primal-dual interior-point relaxation method for nonlinear programs. In the proposed method, the barrier parameter is updated in every step as done in interior-point methods for linear programs, which is prominently different from the existing interior-point methods and the relaxation methods for nonlinear programs. Since our update for the barrier parameter is autonomous and adaptive, the method has potential of avoiding the possible difficulties caused by the unappropriate initial selection of the barrier parameter and speeding up the convergence to the solution. Moreover, it can circumvent the jamming difficulty of global convergence caused by the interior-point restriction for nonlinear programs and improve the ill conditioning of the existing primal-dual interiorpoint methods as the barrier parameter is small. Under suitable assumptions, our method is proved to be globally convergent and locally quadratically convergent. The preliminary numerical results on a well-posed problem for which many line-search interior-point methods fail to find the minimizer and a set of test problems from the CUTE collection show that our method is efficient.Comment: submitted to SIOPT on April 14, 202